Question: A website offers a coupon to $50\%$ of its visitors, selected at random, each day. Yasemin visits the website for $4$ days. What is the probability that Yasemin will not be offered a coupon on at least one of the days she visits the website? Round your answer to the nearest hundredth. $P(\text{at least one day without coupon})=$
Answer: Strategy In this situation it is much easier to calculate the probability of the event we are looking for (at least one day without a coupon) by calculating the probability of its complement (all days with a coupon), and subtracting from $1$. In other words, we can use this strategy: $P(\text{at least one day without coupon})=1-P(\text{all 4 with coupon})$ Calculations $\begin{aligned} &\phantom{=}P(\text{at least one day without coupon}) \\\\ &=1-P(\text{all 4 with coupon}) \\ \\ &=1-0.5^{4} \\ \\ &= 1-0.0625 \\ \\ &= 0.9375\end{aligned}$ Answer $P(\text{at least one day without coupon}) \approx 0.94$